U.S. Navy photo by Mass Communication Specialist 3rd Class Dylan McCord/Released(NEW YORK) -- A tug boat has reached the stricken Carnival cruise ship that is bobbing and listing in the Gulf of Mexico after an engine fire, as currents push the massive ship and its more than 4,000 passengers northward.

The tug has tied up with the Carnival Triumph Monday evening, but will wait until early Tuesday for the expected arrival of a second tug before towing the stricken cruise ship to port.

Carnival said that original plans to haul the crippled ship to Progreso, Mexico, have been scrapped because the ship has drifted about 90 miles north. Instead, the Triumph will be towed to Mobile, Ala.

Meanwhile, the ship, which is 2.5 football fields long, is at the mercy of the sea. The forecast is for 6-foot seas, and it will take the tug boats three full days to haul it back to land.

Carnival spokesman Vance Gulliksen told ABC News that the vessel is listing slightly, 4.5 degrees, because of a 25-knot wind buffeting the ship.

"This listing is to be expected given the wind speed and poses no safety risk," Gulliksen said.

The engine fire that scuttled the pleasure cruise plans of more than 3,000 customers -- the ship also has more than 1,000 crew members -- continues to hobble services on board.

Carnival said its crew has restored auxiliary power, "to operate some basic hotel functions. Currently, public and cabin toilets are operational in certain sections of the ship...and some power in the Lido dining area is providing for hot coffee and limited hot food service."

The Carnival Triumph is now little more than a 100,000-ton cork, bobbing in the Gulf of Mexico without propulsion since the fire broke out Sunday morning. No one was hurt in the fire, but the ship lost power and is relying on a back-up generator.

Brent Nutt said that his wife, Bethany, who is on board, called him to say the plumbing wasn't working on the ship.

"She said there's no running water. They just really got food there to them tonight, and there's no power whatsoever, other than the emergency flasher lights that are on," he said. "She was crying and hysterical."

Sunday's fire was extinguished by an automated system, but not before it hobbled the ship, according to the Coast Guard.

The Carnival Triumph departed Galveston Thursday for a Mexican cruise, which was due to return to the port Monday.

Passengers aboard the wayward ship will receive a full refund, Carnival said, and a voucher for a future cruise with Carnival.